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Crude Fourier Series approximation for PDEs.

  1. Dec 17, 2012 #1
    Is there a way to "crudely" approximate PDEs with Fourier series?

    By saying crudely, I meant this way:

    Assuming I want a crude value for a differential equation using Taylor series;

    y' = x + y, y(0) = 1

    i'd take a = 0 (since initially x = 0),

    y(a) = 1,
    y'(x) = x + y; y'(a) = 0 + 1 = 1
    y"(x) = 1 + y'; y"(a) = 1 + 1 = 2
    y'"(x) = 0 + y"(x); y"'(a) = 0 + 2 = 2

    then y ~ 1 + x + 2/2! x^2 + 2/3! x^3.

    Or something similar to that. Does this crude method have an analog to Fourier-PDE solutions?
     
  2. jcsd
  3. Dec 17, 2012 #2

    chiro

    User Avatar
    Science Advisor

    Hey maistral.

    With a fourier series, you need to project your function to the fourier space to get the co-effecients.

    So the question is, how do you get an appropriate function to project to the trig basis if it's not explicit (i.e. you don't have f(x) but a DE system that describes it)?
     
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